Published online by Cambridge University Press: 28 February 2022
It may be thought that the question ‘when is a physical theory relativistic?’ has a fairly straightforward answer, namely: ‘when it is Galilean invariant’ (for classical mechanics) or ‘Lorentz invariant’ (for special relativity). In the context of the modern ‘spacetime theory’ approach to relativity physics, the answer is more elaborate, in the interests of greater precision. In this paper, we examine two recent discussions of the issue, or aspects of it, found in a 1990 paper of Arntzenius and the well-known 1983 study of Friedman.
Arntzenius constructs a ‘sure-fire method’ of constructing a Lorentz invariant spacetime theory from a non Lorentz invariant one. We argue that if the original theory is anything like a typical dynamical theory in physics, its ‘completeness’—in a sense to be defined—will render the new theory underdetermined.
We wish to thank Tim Budden for stimulating discussions related to the issues raised here.